If there's a better definition of real this won't mean much but here goes.

Let us define 'real' as something that interacts with the world. That is to say, something is real if it has a consequence. Then abstract ideas, such as mathematics, become real things. The consequenses of mathematics can be seen in what they eventually produce: cars, computers, planes, these things require mathematics before they can be designed, let alone built.

Mathematics is simply a form of human thought. It is a tool we (and, presumably, other sapient species, if they exist) use to organize and communicate our thoughts. As such, it is merely a subset of our thoughts and therefore a function of our brain. Mathematics does not interact with the Universe. Our brains do.

Mathematics is simply a form of human thought. It is a tool we (and, presumably, other sapient species, if they exist) use to organize and communicate our thoughts. As such, it is merely a subset of our thoughts and therefore a function of our brain. Mathematics does not interact with the Universe. Our brains do.

Mathematics don't "interact" with the universe, they're laws according to which reality works. Two apples and two more apples is four apples, regardless of our brain.

Mathematics is simply a form of human thought. It is a tool we (and, presumably, other sapient species, if they exist) use to organize and communicate our thoughts. As such, it is merely a subset of our thoughts and therefore a function of our brain. Mathematics does not interact with the Universe. Our brains do.

Mathematics don't "interact" with the universe, they're laws according to which reality works. Two apples and two more apples is four apples, regardless of our brain.

Unless you stuff them in the stomach of a cat which you then put in a box. Then all bets are off.

There are the laws of the Universe. Of which we know approximations. (Probably pretty good, in the case of apple counting, granted.) Those approximations can be put in the form of mathematics. But the mathematics aren't the Laws.

Mathematics is simply a form of human thought. It is a tool we (and, presumably, other sapient species, if they exist) use to organize and communicate our thoughts. As such, it is merely a subset of our thoughts and therefore a function of our brain. Mathematics does not interact with the Universe. Our brains do.

Mathematics don't "interact" with the universe, they're laws according to which reality works. Two apples and two more apples is four apples, regardless of our brain.

No. Mathematics are a method through which we can understand and describe the universe (although mathematics on its own doesn't tell you anything. It has to be paired with real-world data to be useful.) Physics are the laws according to which reality works. We use mathematics to better understand physics, but they're not the same thing.

No, physics is also a method of understanding reality, in terms of equations and forces. The laws of reality are just that- the laws of reality, and there's no way to dumb them down into a science, largely because we're mentally incapable of understanding them all.

No, physics is also a method of understanding reality, in terms of equations and forces. The laws of reality are just that- the laws of reality, and there's no way to dumb them down into a science, largely because we're mentally incapable of understanding them all.

Wow. That's wrong in so many ways I don't know where to begin, especially since you didn't make any actual arguments, just a bunch of assertions.

Suffice it to say that the laws of physics are the laws of reality, that science (which relies heavily on mathematics) is our best method of understanding them, and that there's absolutely no reason to believe that we're somehow "mentally incapable" of understanding those laws fully at some point. We're constantly making progress in our understanding of these laws and there's been no indication of some sort of looming barrier to our understanding that we won't be able to pass through.

First of all, there's a difference between the science known as physics and the actual laws of physics.
And I feel we're incapable of understanding them in total not because of some magical mental barrier (though that's part of it; how many people really understand how the 7th dimension works?), so much as the fact that there doesn't seem to be any visible limit to them.

When discussing math one must keep in mind that numbers are only what they are because that is what a majority of humans say that they are. Imaginary numbers are a good examble. I stands for the square root of negative one, but if you got enough people to agree with you you could say that one is actually the square root of negative one. Another example, which I got from the book 1984, could be that while currently people would say that there is one smilely here with the right people saying otherwise it could actually be called three. Therefore numbers exist, but are only real for as long as we say they are, at which point they will also cease to exist.

When discussing math one must keep in mind that numbers are only what they are because that is what a majority of humans say that they are. Imaginary numbers are a good examble. I stands for the square root of negative one, but if you got enough people to agree with you you could say that one is actually the square root of negative one.

Only in Z/2Z.

Quote:

Another example, which I got from the book 1984, could be that while currently people would say that there is one smilely here with the right people saying otherwise it could actually be called three. Therefore numbers exist, but are only real for as long as we say they are, at which point they will also cease to exist.

I think you may be missing my point. The reason you say that three is three is because that is what you've been taught to believe. we've been brought up in a society that says that this, , is three. All I'm saying is that if someone was brought up differently then when you asked them how many three was they would say it was this, . If you follow.

I think you may be missing the entire concept of mathematics. I can't tell if your point is that you can choose to call three by some other name, in which case you're arguing nomenclature, which is orthogonal to the current argument<sup>1</sup>, or if you mean to suggest that mathematics itself isn't invariant as most people are taught to believe. If you mean the latter, then let me assure you of your error; mathematics is indeed invariant between cultures, provided both cultures are advanced enough to develop it.

There is really only one major leap of faith you have to take in order to prove the existence of "three". You have to believe in the existence of "one". The unit. Anything, really, as long as you accept that it exists and can be dealt with as an individual thing. You can deny that anything at all exists, and it indeed becomes impossible to count things.

However, if you acknowledge that something (let's call it '1') exists, then you can put another something with it<sup>2</sup> (we'll call this activity '+'), and then yet another something, and you have more than one somethings. For convenience, we all agree that this is '3'. You can choose to call it speeblarg, or "one", but nomenclature alone cannot change the fundamental fact that there are --> <-- this many.

The actual basis of mathematics, at least as discussed in this thread, is rooted in set theory, and contains a small fixed number of "postulates" which are generally considered to be self-evident, but must ultimately be taken on faith. Everything else follows logically and deductively from these postulates. If you want to successfully attack mathematics, you have to do it here.

<sup>1</sup> If you do not start with a common assumed nomenclature, then no communication is possible. Therefore, to argue that three may not be three due to a difference in nomenclature is spurious, and not a useful argument. The essence of communication (and thus the argument) carries with it an underlying assumption that all parties have a common vocabulary. You can neither communicate, nor (by induction) argue without one<sup>3</sup>.

<sup>2</sup> Not completely true - you can also deny the possibility of addition, as that is yet another of the fundamental postulates. However, I was trying to keep the argument simple.

<sup>3</sup> Ironically, this is the same spot where I see the fundamental disconnect form in many a political or religious "argument". Two sides will argue logical extensions which are both true from their point of view, because they did not begin by agreeing on common assumptions and definitions.

The actual basis of mathematics, at least as discussed in this thread, is rooted in set theory, and contains a small fixed number of "postulates" which are generally considered to be self-evident, but must ultimately be taken on faith.

A slight quibble: It's not the postulates themselves that have to be assumed; it's a formal system, and you can start with whatever axioms you like. What you have to assume is that the postulates accurately describe and relate to the real world and our notions of real world sets.